Question

In the adjoining figure, D is the midpoint of side BC of $\Delta ABC$ and E is the mid-point of BD. If O is the mid-Point of AE, then find whether the area of $\Delta OBE=\frac{1}{8}$ area of $\Delta ABC$ is true/false.

• A. True
• B. False

Answer 1

The correct option is A True

$In\Delta ABC,D\text{is the mid point of BC, E is the mid point of BD and O is the midpoint of AE}$
$\text{Then}\text{BE=}\frac{1}{4}BCorOE=\frac{1}{2}AE$
$Weknowareaoftriangle=\frac{1}{2}hb$
$Areaof\Delta ABC=\frac{1}{2}\left(BC\right)\left(AE\right)$
$Areaof\Delta BOE=\frac{1}{2}\left(BE\right)\left(OE\right)$
$Thenareaof\Delta BOE=\frac{1}{8}areaof\Delta ABC$
$H\text{ence the given statement is true}\text{.}$